Delta Modulation is subject to two types of quantization error
- slope Overload Distortion (SOD)/ Slope Overload error
- Granular Noise / Granular error.
During the process of digital equivalent integration of x(t) that is approximating x(t) with there exists an error called Quantization error as shown by
if time instance is (n-1)th instance.
the Quantization error q[n] is of two types in Delta Modulation.
- Slope-Overload Distortion:- if the rate of rise of input signal is so high
i.e, the slope of the signal is so high so that the stair case signal can not approximate to x(t) .
i.e, as is large enough
in this case the step size becomes to small for the stair case approximation to follow a steep segment of the input wave form x(t) with the result that falls behind which can be clearly visible in the figure.
the Qunatization error that exist between x(t) and in this condition is called as slope overload distortion.
Generaaly DM is often referred as a linear Delta Modulator because the step size is fixed during approximation process, and also its maximum (or) minimum slopes occur along straight lines.
To avoid slope Overload Distortion, step size must be increased.
Granular Noise (or) Idle Noise:-
In contrast to slope overload distortion Granular noise occurs when the step size is too large relative to the local slope characteristic of the input wave form x(t)
∴ This large value of causes that the stair case approximation to hunt around a flat segment of the input wave form as shown in the above figure
i.e, oscillates between when. x(t) is almost straight.
∴ The error between and in this condition is called as Granular noise (or) Idle noise.
To eliminate this error is to make the step size small.
Granular noise occurs that for a very small variations in the input signal causes a very large variations in the approximated signal .
Thus we see that there is a need to have a large step size to accomodate a wide dynamic range of input signal.
and a small step size is required to accurate representation of relatively low-level signals.
i.e, large step size is required to reduce slope overload distortion and small step size is required to reduce Granular noise.
∴ It is clear that the choice of the optimum step size that minimizes the Mean Square value of the Quantization error in a Linear Delat Modulator will be the result of a compromise between Slope overload Distortion and Granular Noise.
To satisfy such a requirement , we need to make the Delta modulator “Adaptive” in the sense that the step size is made to vary in accordance with the input signal x(t).
This can be further discussed in the topic called as “Adaptive Delta Modulation ” scheme (ADM).
